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Omni-MATH / Let n be an integer of the form a²+b², where a and b are relatively prime integers and such that if p is a prime, p≤√(n), then p divides ab. Determine all such n.

Problem

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problem

Let nn be an integer of the form a2+b2a^{2}+b^{2}, where aa and bb are relatively prime integers and such that if pp is a prime, p≤np \leq \sqrt{n}, then pp divides aba b. Determine all such nn.
Plain-text mathematical notation (without MathML)
Let n be an integer of the form a²+b², where a and b are relatively prime integers and such that if p is a prime, p≤√(n), then p divides ab. Determine all such n.
Original LaTeX notation
Let $n$ be an integer of the form $a^{2}+b^{2}$, where $a$ and $b$ are relatively prime integers and such that if $p$ is a prime, $p \leq \sqrt{n}$, then $p$ divides $a b$. Determine all such $n$.

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Source and history

task_id
54379d38-db84-519a-8812-1952e4b875ce
task_key
test--54379d38-db84-519a-8812-1952e4b875ce
task_revision_id
1
config / split
/ test

Official source

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